Generally Extraordinary Ministers of Holy Communion cannot consume the remaining Precious Blood in their chalices.
From the 2010 General Instruction of the Roman Missal (GIRM) approved for Australia:
“284. … b. whatever may remain of the Blood of Christ is consumed at the altar by the Priest or the Deacon or the duly instituted acolyte who ministered the chalice.”
An exception is in the USA, if the diocesan bishop approves. This is because the Vatican has approved “Norms for the Distribution and Reception of Holy Communion under Both Kinds in the Dioceses of the United States of America,” which includes:
“52. When more of the Precious Blood remains than was necessary for Communion, and if not consumed by the bishop or priest celebrant, “the deacon immediately and reverently consumes at the altar all of the Blood of Christ which remains; he may be assisted, if needs dictate, by other deacons and priests.” When there are extraordinary ministers of Holy Communion, they may consume what remains of the Precious Blood from their chalice of distribution with permission of the diocesan bishop.”
If there is an exceptional situation of more consecrated wine than the priests, deacons and instituted acolytes can consume, then as reported in the USCCB Bishops’ Committee on the Liturgy Newsletter of March/April 2002:
"With respect to the second request, Cardinal Medina, Prefect of CDWDS, noted that neither an indult nor even the permission of the diocesan bishop is required for extraordinary ministers of Holy Communion to help the priest celebrant to consume what may remain of the Precious Blood after the distribution of Holy Communion. “Rather,” he wrote, “given the grave and overriding need to safeguard the Precious Blood, ministers of Holy Communion or other communicants may consume what remains of the Precious Blood in a dignified and reverent manner.”